Having a mini shopping cart is definitely not an alternative to the full page cart as decision making will be tedious with just a mini cart. It will help shoppers keep track of how much they spend and what they buy. Provide a link in the mini cart to view the full page cart instead of taking the user directly to checkout.
Use mini cart to confirm that a product has been added to cart. You can also include product recommendations which would make it easier for your shoppers to find more products.